This dissertation presents a fast electromagnetic field-circuit simulator that permits the full-wave modeling of transients in microwave systems containing multiscale structures and nonlinear devices. This time-domain simulator is composed of two components: (i) a full-wave solver that models interactions of electromagnetic fields with conducting surfaces and finite dielectric volumes by solving time-domain surface and volume electric field integral equations, respectively, and (ii) a circuit solver that models currents and voltages in lumped circuits, which are potentially active and nonlinear, by solving Kirchoff's equations through modified nodal analysis. The simulator also supports multiport transfer-function blocks (macromodels), which model (lumped or distributed) linear, time-invariant, multi-input multi-output subsystems that are connected to ports modeled by either the full-wave solver or the circuit solver. These field and circuit analysis components are interfaced and the resulting coupled set of nonlinear equations is evolved in time by a multidimensional Newton-Raphson scheme. The solution procedure is accelerated by allocating field- and circuit-related computations across the processors of a distributed-memory cluster, which communicate using the message-passing interface standard. Furthermore, the electromagnetic field solver, whose demand for computational resources far outpaces that of the circuit solver, is accelerated by an FFT-based algorithm, viz. the time-domain adaptive integral method. The resulting parallel FFT-accelerated transient field-circuit simulator is used to (i) analyze electromagnetic scattering from large-scale structures, including an aircraft shell, (ii) characterize microwave circuits with nonlinear devices, including a power-combining array, and (iii) quantify system-level electromagnetic interference for systems with multiple scales of details, including an antenna array on a cockpit.